Question

evaluate (729/512)^-2/3​

Answer 1

Answer:

0.79

Step-by-step explanation:

${( \frac{729}{512}) }^{ \frac{ - 2}{3} } \\ = {( \frac{512}{729} )}^{ \frac{2}{3} } \\ = { (\frac{8}{9} )}^{3 \times \frac{2}{3} } \\ = {( \frac{8}{9}) }^{2} \\ = \frac{64}{81} \\ = 0.79$

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Answer 2

Step-by-step explanation:

$\bf \underline{Solution-}$

$\textsf{Given,}$

$\sf{ \bigg( \frac{729}{512} \bigg) ^{ - \frac{2}{3} } }$

$\sf{ \Rightarrow \: \frac{1}{(729 {)}^{ \frac{2}{3} } } \times (512 {)}^{ \frac{2}{3} } }$

$\sf{ \Rightarrow \: \frac{(512 {)}^{ \frac{2}{3} } }{(729 {)}^{ \frac{2}{3} } } }$

$\sf{ \Rightarrow \: \frac{( {8}^{3} {)}^{ \frac{2}{3} } }{( {9}^{3} {)}^{ \frac{2}{3} } } }$

$\sf{ \Rightarrow \: \frac{ {8}^{ \cancel{3} \times \frac{2}{ \cancel{3}} } }{{9}^{ \cancel{3} \times \frac{2}{ \cancel{3}}}} }$

$\sf{ \Rightarrow \: \frac{ {8}^{2}}{{9}^{2} }}$

$\sf{ \Rightarrow \: \frac{8 \times 8}{9 \times 9} }$

$\sf{ \Rightarrow \: \frac{64}{81} \: \: \bf{Ans.} }$